You're given a sequence of N distinct integers. You need to find a subsequence of length K with the maximum possible median.

The median of a sequence is the value of the element which is in the middle of the sequence after sorting it in non-decreasing order. If the length of the sequence is even, the left of two middle elements is selected. For example, if the sequence is [3, 4, 2, 1, 5], then the median is 3 since after sorting, it will look like [1, 2, 3, 4, 5] and 3 is the only middle element. The median of [4, 2, 1, 5] is 2 since after sorting, the value 2 is the left of the two middle elements 2 and 4.

A subsequence is a sequence that can be derived from the given sequence by deleting zero or more elements without changing the order of the remaining elements. For example, if the sequence is [2, 1, 4, 5, 7], then [1, 5, 7], [2, 1, 4], [5] are some valid subsequences but [4, 1, 2], [1, 6, 7] are not.

------ Input Format ------

• The first line will contain T, the number of test cases. The description of test cases follow.
• The first line of each test case consists of two space-separated integers N, the length of the sequence, and K, the length of the subsequence to be found.
• The second line of each test case consists of N distinct space-separated integers A_{i}, the elements of the sequence.

------ Output Format ------

• For each test case, output two lines.
• The first line should consist of the median of the subsequence with the maximum median.
• The second line should consist of K space-separated integers, representing a subsequence with that median. If there are multiple such subsequences, print any.

------ Constraints ------

$1 ≤ T ≤ 30$
$1 ≤ K ≤ N ≤ 2 \times 10^{5}$
$1 ≤ A_{i} ≤ 10^{9}$
- Sum of $N$ over all test cases won't exceed $5 \times 10^{5}$

----- Sample Input 1 ------
1
5 3
1 4 3 6 5
----- Sample Output 1 ------
5
1 6 5

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